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Suppose you are fitting a linear model which has heteroskedastic (non-constant) residuals. I have read that there are a number of ways of dealing with this situation, including Weighted Least Squares (WLS) estimation and applying Box-Cox and/or Box Tidwel transformation.

As far as I understand, the WLS computes weights and assigns them to each observation as to make spread of residuals more constant. For example, data points with large residuals receive lower weights.

The Box-Cox transformation is essentially a power transformation to the DV: the y variable. The Box-Tidwel transforms the IVs: X variables to make their relation with Y linear.

What I am interested in is in which cases would you prefer WLS over transformations and vice versa? Or is it simply a trial-and-error process of trying different methods? Some intuitive and experience-based explanations would be very much appreciated.

PsychometStats
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    Hopefully you'll get a much better answer than I can give you. I think current thinking is to not use transformations, but to either use an appropriate generalized linear model or to use a method like WLS. You might also look into methods that adjust for heteroscedasticity. For one-way designs there's Welch's anova. And R offers white-ajusted anova for heteroscedasticity. There's lots of discussion here: https://stats.stackexchange.com/a/91881/166526 – Sal Mangiafico Oct 11 '19 at 02:32
  • @SalMangiafico thank you for your reply! I greatly appreciate it! – PsychometStats Oct 11 '19 at 02:55

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